"This is a lady mayor who asked for $127 million of hazard mitigation money from the governor to give that to her from the federal money. When the state was only receiving in its entirety $300 million," Barbour told CNN, adding that her accusations were "absurd."

"Well I didn't mean for it to be taken the wrong way," he responded. "Somebody wrote me a note about it, I wrote her back and said thanks for the constructive criticism."

Pressed by Todd to say whether he believed the comment was wrong, Barbour said he didn't think it was "beneficial."

"There's certainly no difference between a lady mayor and a man mayor," he added. "Except in this Christie story, the first person was a mayor [Fort Lee, N.J. Mayor Mark Sokolich] who happened to be a man. The second person was a mayor who happened to be a lady, and you don't want to get them mixed up. But that wasn't the right way to go in it."